r 



Low Frequency and their Resonance. 509 



coils in the manner just described was for the purpose of avoid- 

 ing the brush discharges between the primary and the sec- 

 ondary coils. He does not seem to have been aware at that 

 time of the fact that by this method of arranging the two coils 

 it is possible to obtain another and probably quite as important 

 advantage, namely : to diminish the number of turns in the 

 secondary coil very much and thus diminish its resistance, 

 capacity and self-induction and all the evils connected therewith 

 and therefore to increase the secondary terminal capacity and po- 

 tential. In such an arrangement the relations of (l0 a ) are very 

 nearly true and the nearer they are to the truth the higher will 

 be the output and the efficiency of the high frequency system. 



These few observations will suffice to point out that on the 

 one hand the high frequency currents as developed by Mr. 

 Tesla are resonant • electrical oscillations, whose period is very 

 long in comparison to the period of Herzian oscillations, and 

 that on the other hand their mathematical theory is simply the 

 theory of the ordinary low frequency resonance given in this 

 and the preceding paper. 



It is my pleasant duty to thank Mr. Tesla on this occasion 

 for the favor which he conferred upon me by lending me his 

 remarkable apparatus for a few days. My short experience 

 with it has taught me many an instructive lesson for which I 

 feel very grateful to Mr. Tesla. 



Before describing some of my experiments on resonance in 

 mutually inductive circuits with low frequency impressed 

 e. m. f. it seems desirable to point out the relations in mutually 

 inductive circuits when the primary circuit contains no con- 

 denser. 



When an alternator containing iron in the armature is em- 

 ployed to generate the impressed e. m. f. then this method of 

 arranging the circuits must be adopted in experiments on res- 

 onance, especially when the frequency is over 100 periods per 

 second. The reason for this will be apparent further below. 

 For this arrangement of the circuits we shall have when reso- 

 nance is established in the secondary circuit 



ES . . . , . 



= sin \pt,— <p) (13) 



V> 2 L 2 S 2 + (p 2 M 2 + RS) 



y — P ... _ si n i pt _ ,p\ ( 14 ) 



V> 2 L 2 S 2 + (p 2 M 2 + RS) 2 



pLS 



tan cp = — cot ip = 



jt? 2 M 2 + RS' 



Hence cp =i — + ip. 



